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arXiv · 2404.08822

The characteristic sequence of the integers that are the sum of two squares is not morphic

Shuo Li
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Abstract

Let $(s_2(n))_{n\in \mathbb{N}}$ be a $0,1$-sequence such that, for any natural number $n$, $s_2(n) = 1$ if and only if $n$ is a sum of two squares. In a recent article, Tahay proved that the sequence $(s_2(n))_{n\in \mathbb{N}}$ is not $k$-automatic for any integer $k$, and asked if this sequence can be morphic. In this note, we give a negative answer to this question.

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Shuo Li. 2024-04-12. The characteristic sequence of the integers that are the sum of two squares is not morphic. https://arxiv.org/abs/2404.08822

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